This assumes that the discovery curve is sigmoidal, with the x-axis being time and the y-axis being number of genera known. It also assumes that our concept of what constitutes a genus won't change, that the peak should be defined in terms of genera instead of species, and that birds aren't dinosaurs.

"Since humans started searching for dinosaur bones in 1824, it's estimated that we've found remnants from 29 percent of these types, mostly in the last 20 years ... If we keep at the current pace of new discovery, it's likely that we'll hit something like "peak dinosaur," with 50 percent of all dinosaur genera discovered, by 2037."